Is it permissible to shake hands with a disbeliever or a Dhimmi, to help a disbelieving woman if she falls, and to offer a disbeliever a seat on the bus?

Shaking hands with a disbeliever is disliked (makrooh). It is not permissible to touch a disbelieving woman except in cases of extreme necessity, such as fearing for her destruction and there being no one else to save her. If a person is a disbeliever, do not stand up from your place as a sign of veneration for him. As for a Muslim, there is no harm in honoring him by standing up, especially if he is an elderly shaykh.